Scattering relations for point sources: Acoustic and electromagnetic waves

The problem of scattering of spherical waves by a bounded obstacle is considered. General scattering theorems are proved. These relate the far-field patterns due to scattering of waves from a point source put in any two different locations. The scatterer can have any of the usual properties, penetrable or impenetrable. The optical theorem is recovered as a corollary. Mixed scattering relations are also established, relating the scattered fields due to a point source and a plane wave.